Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties

Izak Broere, Jozef Bucko, and Peter Mihók. "Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties." Discussiones Mathematicae Graph Theory 22.1 (2002): 31-37. <http://eudml.org/doc/270442>.

@article{IzakBroere2002,
abstract = {Let ₁,₂,...,ₙ be graph properties, a graph G is said to be uniquely (₁,₂, ...,ₙ)-partitionable if there is exactly one (unordered) partition V₁,V₂,...,Vₙ of V(G) such that $G[V_i] ∈ _i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (₁,₂,...,ₙ)-partitionable graphs exist if and only if $_i$ and $_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ 1,2,...,n.},
author = {Izak Broere, Jozef Bucko, Peter Mihók},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {induced-hereditary properties; reducibility; divisibility; uniquely partitionable graphs.; partitionable graphs; graph properties; partition; irreducible properties},
language = {eng},
number = {1},
pages = {31-37},
title = {Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties},
url = {http://eudml.org/doc/270442},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Izak Broere
AU - Jozef Bucko
AU - Peter Mihók
TI - Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties
JO - Discussiones Mathematicae Graph Theory
PY - 2002
VL - 22
IS - 1
SP - 31
EP - 37
AB - Let ₁,₂,...,ₙ be graph properties, a graph G is said to be uniquely (₁,₂, ...,ₙ)-partitionable if there is exactly one (unordered) partition V₁,V₂,...,Vₙ of V(G) such that $G[V_i] ∈ _i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (₁,₂,...,ₙ)-partitionable graphs exist if and only if $_i$ and $_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ 1,2,...,n.
LA - eng
KW - induced-hereditary properties; reducibility; divisibility; uniquely partitionable graphs.; partitionable graphs; graph properties; partition; irreducible properties
UR - http://eudml.org/doc/270442
ER -